- Source: Thermal conductance quantum
In physics, the thermal conductance quantum
g
0
{\displaystyle g_{0}}
describes the rate at which heat is transported through a single ballistic phonon channel with temperature
T
{\displaystyle T}
.
It is given by
g
0
=
π
2
k
B
2
T
3
h
≈
(
9.464
×
10
−
13
W
/
K
2
)
T
{\displaystyle g_{0}={\frac {\pi ^{2}{k_{\rm {B}}}^{2}T}{3h}}\approx (9.464\times 10^{-13}{\rm {W/K}}^{2})\;T}
.
The thermal conductance of any electrically insulating structure that exhibits ballistic phonon transport is a positive integer multiple of
g
0
.
{\displaystyle g_{0}.}
The thermal conductance quantum was first measured in 2000. These measurements employed suspended silicon nitride (Si3N4) nanostructures that exhibited a constant thermal conductance of 16
g
0
{\displaystyle g_{0}}
at temperatures below approximately 0.6 kelvin.
Relation to the quantum of electrical conductance
For ballistic electrical conductors, the electron contribution to the thermal conductance is also quantized as a result of the electrical conductance quantum and the Wiedemann–Franz law, which has been quantitatively measured at both cryogenic (~20 mK) and room temperature (~300K).
The thermal conductance quantum, also called quantized thermal conductance, may be understood from the Wiedemann-Franz law, which shows that
κ
σ
=
L
T
,
{\displaystyle {\kappa \over \sigma }=LT,}
where
L
{\displaystyle L}
is a universal constant called the Lorenz factor,
L
=
π
2
k
B
2
3
e
2
.
{\displaystyle L={\pi ^{2}k_{\rm {B}}^{2} \over 3e^{2}}.}
In the regime with quantized electric conductance, one may have
σ
=
n
e
2
h
,
{\displaystyle \sigma ={ne^{2} \over h},}
where
n
{\displaystyle n}
is an integer, also known as TKNN number. Then
κ
=
L
T
σ
=
π
2
k
B
2
3
e
2
×
n
e
2
h
T
=
π
2
k
B
2
3
h
n
T
=
g
0
n
,
{\displaystyle \kappa =LT\sigma ={\pi ^{2}k_{\rm {B}}^{2} \over 3e^{2}}\times {ne^{2} \over h}T={\pi ^{2}k_{\rm {B}}^{2} \over 3h}nT=g_{0}n,}
where
g
0
{\displaystyle g_{0}}
is the thermal conductance quantum defined above.
See also
Thermal transport in nanostructures
References
Kata Kunci Pencarian:
- Thermal conductance quantum
- Conductance quantum
- Thermal conductivity and resistivity
- Quantum electrochemistry
- Thermal conduction
- Quantum wire
- Quantum point contact
- Electrical resistance and conductance
- Graphene
- Bolometer
